Home #1 Mathematics Can we prove ... from a Mathematical point of view that Waves has ... a Wave form (like Sin and Cos) ? ...
Can we prove ... from a Mathematical point of view that Waves has ... a Wave form (like Sin and Cos) ? ... PDF Print E-mail
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Wednesday, 18 May 2011 16:10

 

Greetings,

      A Wave in the Sea ... or a Wave inside a glass of water ... all ... are waves. Still the very topography of the cities, buildings, cars, mountains and flowers ... as wells animals and we humans are measured ... in waves.

      Before to start ... let me push a new question. Can the Heat be measured in waves? ... and the answer is immediate and is Yes!

      The excellent book,

    

(Click to read the book. Chapter discussed here is Chapter 5 - pag. 474)

      offers an excellent as well exhaustive explanation solving the Heat and Wave Partial Differential Equations using the Separation of variables and the Fourier Serie.

       In fact, the Heat Equation is the following,

       and is similar to the Wave Equation,

        Now, let me figure out for you ... the Solution.

       

           Reading the book (is not complex, only Calculus is required) we can reach that the solution for the Heat Equation is,

          

      Returning now to the Wave Equation,

      We have that,

 

      I, Giovanni say ... is now clear that the Wave,

      has

    which are similar to the Harmonograph (that are the representation of music ... in form)

     which equation is,

      The Graphical Representation of a Fourier Serie is ...

     and this is close to an Electro-Cardiogram

 

Thanks ...

Giovanni A. Orlando.

PS> You may wonder to read the original book of Joseph Fourier ... in English, Joseph Fourier - Theory Analytical of Heat.pdf

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Last Updated on Wednesday, 18 May 2011 17:30